Thursday, May 17, 2012

FORM & FORMALISM III: FORMALISATION & DIALECTICS

ANNOUNCEMENT:

On June 7th and 8th, at the JVE in Maastricht, the Netherlands, the third Form & Formalism conference will be taking place, under the title Formalisation & Dialectics. Pasted below are the manifesto, schedule and poster for the conference (designed by Mary Ikoniadou).

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It has been two hundred years since the glacial drift of syllogistics gave way
to the unsteady movements of science, a double revolution that would both
revive and divided the discipline of logic. Two texts served to mark the
irreversible thresholds that logic had crossed: Hegel’s Science of Logic in
1812, and Boole’s Mathematical Analysis of Logic in 1847.

Were it not for Hegel’s own excessive resistance to the idea of mathematising logic – an idea not yet realised before his death – the most doctrinaire
dialectician would no doubt expect the eventual synthesis of these anti-
thetical trajectories in a ‘higher unity’. On this score, however, history has been meek. The two traditions issuing from the logical revolts of the
nineteenth century – the tradition of mathematical logic, on the one hand,
and dialectical logic on the other. By the twentieth century, the gulf
between The Algebra Of Revolution announced by Herzen and Lenin, and
The Revolution In Algebra begun by Grassmann and Boole had become
almost entirely void of communication. Dialectical philosophers, with a
handful of brilliant exceptions, would become increasingly oblivious to the
events unfolding in the mathematical science of logic, while mathematical
logicians, again with rare and ingenious exceptions, would become
increasingly unconcerned with the demands of dialectical philosophy.

It is this situation that we wish to interrupt.

If dialectics is to be reanimated, today, we must cross it at is point of
greatest resistance, a blind spot formed by a resistance to mathematics:
the idea, which Hegel resisted furiously despite the embryonic status in
which his time retained it, of logical calculation.

It was through this idea that history would give birth to another that is
ultimately more profound: the idea of logico-mathematical formalisation,
an idea that would liberate mathematical thought from the contingency
of its objects, through an act of reflection that would make it itself a mathematical object. This would, moreover, be a reflection subject to an
essentially dialectical drama, slipping away from its own grasp, a refractory
reflection that would generate antinomies, incompletions and subversions
of meaning. Through this struggle to apprehend itself as such, mathematical logic would, quietly, and without attracting the attention of either of
the two traditions that the nineteenth century began, rebuild the dialectic
from the calculi Hegel rejected.

The purpose of this conference is, first and foremost, to draw philosophy’s
attention to this reanimation of the dialectic from the ‘dead bones’ of
calculation, to accelerate this reanimation through careful experiments
in formalisation, and interrupt the servitude to ‘the understanding’ to
which philosophers have, for the last century, indentured mathematical
logic. If philosophy wishes to find in logic something other than a regimentation of the understanding’s prejudices, then the task of tapping the underground current of the dialectic in mathematical logic the
logico-mathematical force latent in dialectical philosophy, is one we
can no longer ignore.